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ERG - Marie Curie actions-European Re-integration Grants

Objective

On a compact Riemannian manifold without boundary, the Laplace and Dirac operators have discrete spectra accumulating towards infinity. The eigenvalue counting function has an asymptotic expansion depending on the volume and the dimension of the manifold. On noncompact manifolds several aspects of this theory may go wrong. In a recent paper we proved that on manifolds with conformally asymptotically cylindrical ends, a more general Weyl law holds for the eigenvalues of the Dirac operator. The goal of this p roject is to investigate whether such laws hold on other types of Riemannian manifolds with singularities, in particular manifolds with corners with conformally cuspidal ends, and conformally conical manifolds.